Spontaneous radiation emission from short, high field strength magnetic devices

Since the earliest papers on undulators were published, it has been known how to calculate the spontaneous emission spectrum from short undulators when the magnetic field strength parameter is small compared to unity, or in “single” frequency sinusoidal undulators where the magnetic field strength parameter is comparable to or larger than unity, but where the magnetic field amplitude is constant throughout the undulator. Fewer general results have been obtained in the case where the magnetic device is both short, i.e., the magnetic field strength parameter changes appreciably throughout the device, and the magnetic field strength is high enough that ponderomotive effects, radiation retardation, and harmonic generation are important physical phenomena. In this paper a general method is presented for calculating the radiation spectrum for short, high-field magnetic devices. It is used to calculate the emission from some designs of recent interest.